Answer:
83.35 feet above ground.
Step-by-step explanation:
Please find the attachment.
We have been given that Hudson (3 feet tall) is on the beach flying a kite. His angle of elevation looking up to the kite is 40 degrees. The kite string is 125 ft long.
We can see that the string of kite forms a right triangle with an angle of elevation (40 degrees) as shown in the attachment.
To solve for h, we will use sine as sine related opposite side of a right triangle with hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(40^{\circ})=\frac{h}{125}[/tex]
[tex]h=125\cdot \text{sin}(40^{\circ})[/tex]
[tex]h=125\cdot 0.642787609687[/tex]
[tex]h=80.348451210875\approx 80.35[/tex]
To find the height of kite off the ground, we will add height of Hudson to 80.35 feet as well as he is flying the kite.
[tex]80.35+3=83.35[/tex]
Therefore, the kite is approximately 83.35 feet above ground.
